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<b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xxreal_0.html#V3">negative</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:12"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" target="_self">Tdisk</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="brouwer.html#K2" target="_self">Tdisk</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<a NAME="E2:12"/><i><font color="Green">E9</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="toprealb.html#T9">TOPREALB:9</a></i>;<br/>
<a NAME="E3:12"/>
 <a href="brouwer.html#K3" target="_self">HC</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="topreal9.html#K4">halfline</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal9.html#K3">Sphere</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="brouwer.html#E1:12"><i><font color="Green">E8</font></i></a>, <a class="ref" href="brouwer.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:12"/>
 <a href="brouwer.html#K3" target="_self">HC</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7">Tcircle</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="brouwer.html#E2:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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